SCFT Study of Microphase Separation in Mixed Polymer Brushes Grafted on Cylindrical Surface

Abstract

We report on microphase separation behaviors of mixed polymer brushes grafted onto an infinitely long cylindri- cal rod by performing polymer self-consistent field theory (SCFT) calculation with "masking" technique. The "masking" technique is especially suitable to deal with systems of confined polymers grafted onto curved surfaces. We have developed a method to solve the morphology of block copolymers confined into complicated topographic surfaces with SCFT. In this paper, this unique technique is extended to solve the SCFT for nanorod grafted by mixed polymer brushes. Furthermore, the use of simple Cartesian grids in a cubic computational cell with periodic boundary conditions makes it possible to solve dif- fusion equations in SCFT by utilizing an efficient and highly accurate pseudo-spectral method involving fast Fourier trans- form. Both parallel rippled phase and ring-shaped phase are predicted. We have investigated the influences of the cylinder radius, grafting density and interaction between the two incompatible grafting polymers on the stability of the two typical phases. Our results show that the system prefers the ring-shaped phase with the increase of the cylinder radius, grafting den- sity and interaction between the two grafting polymers. Phase diagrams involving these parameters are constructed, and we explain the reason of the transition between the parallel rippled phase and ring-shaped phase in terms of the degree of phase segregation. Again, the degree of phase segregation is higher with larger cylinder radius, grafting density and interaction between the two grafting polymers. By comparing the degree of phase segregation and free energy of the parallel rippled and ring-shaped phases at the same condition, we found that the ring-shaped phase favors the entropic part of the free energy while the parallel rippled phase significantly reduces the enthalpy. Therefore, when the degree of phase segregation is low, the free energy of the system is dominated by the enthalpy, leading to the parallel rippled phase; when the degree of phase segregation is high, the free energy of the system is dominated by the entropic part and the ring-shaped phase is stable. We also found that the domain numbers of parallel rippled phase and the period of alternating ring-shaped phase vary with the radius of cylinder. These predictions are expected to be helpful in rational design and fabrication of such novel polymer brushes.